Problem: Reduce to lowest terms: $ \dfrac{3}{4} \div - \dfrac{1}{2} = {?}$
Answer: Dividing by a fraction is the same as multiplying by the reciprocal of the fraction. The reciprocal of $- \dfrac{1}{2}$ is $- \dfrac{2}{1}$ Therefore: $ \dfrac{3}{4} \div - \dfrac{1}{2} = \dfrac{3}{4} \times - \dfrac{2}{1} $ $ \phantom{ \dfrac{3}{4} \times - \dfrac{2}{1}} = \dfrac{3 \times -2}{4 \times 1} $ $ \phantom{ \dfrac{3}{4} \times - \dfrac{2}{1}} = \dfrac{-6}{4} $ The numerator and denominator have a common divisor of $2$, so we can simplify: $ \dfrac{-6}{4} = \dfrac{-6 \div 2}{4 \div 2} = -\dfrac{3}{2} $